Generally speaking, for model-based method, we assume that we have known the transforming probability of states. But for model-free RL, we know nothing about the transition probability. As a result, model-free RL is more like a black-box. And it's with more freedom but needs more data to train as well.

University of Michigan - Ann Arbor

Classification of Reinforcement Learning Methods

https://cims.nyu.edu/~donev/Teaching/WrittenOral/Projects/XintianHan-WrittenAndOral.pdf
https://www.davidsilver.uk/teaching/     
(David Silver's tutorial of reinforcement learning)
http://rail.eecs.berkeley.edu/deeprlcourse/
https://katefvision.github.io/
http://incompleteideas.net/rlai.cs.ualberta.ca/RLAI/RLAIcourse/RLAIcourse2006.html
http://web.stanford.edu/class/cs234/schedule.html

Useful Tutorials about Math behind Reinforcement Learning

Advantages:
High efficiency of data utilization. It's used to approximate the known model, so it's more explainable.
Disadvantages:
Hard to use and construct. Easy to be over-fitting. It's with lower asymtotic performance.

Pros and Cons of Model-based RL Algorithm

Model-based RL vs Model-free RL

These kind of methods are widely used in one-shot learning area. Practically speaking, it's also widely used to approximate control model, robotics area and chess playing area.

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